具有食饵选择的食物链模型的定性分析

李娅; 胡含嫣; 林君仪

doi:10.13700/j.bh.1001-5965.2015.0642

具有食饵选择的食物链模型的定性分析

doi: 10.13700/j.bh.1001-5965.2015.0642

1.
北京航空航天大学数学与系统科学学院, 北京 100083
2. 肯特大学数学、统计与精算学院, 坎特伯雷 CT27NZ
3. 北京大学数学科学学院, 北京 100871

基金项目: 中央高校基本科研业务费专项资金（30361201，30458701）

详细信息

作者简介:
李娅,女,博士,讲师。主要研究方向:生物数学和动力系统。Tel.:15801211607,E-mail:yli@buaa.edu.cn

通讯作者:
李娅,Tel.:15801211607,E-mail:yli@buaa.edu.cn

中图分类号: O29;O193
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- 文章访问数: 817
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- 被引次数: 0
出版历程
- 收稿日期: 2015-09-28
- 网络出版日期: 2016-10-20

Qualitative analysis of a food chain model with alternative prey

LI Ya^{1
, ,},
HU Hanyan²,
LIN Junyi³

1.
School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
2. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT27NZ, United Kingdom
3. School of Mathematics, Peking University, Beijing 100871, China

Funds: the Fundamental Research Funds for the Central Universities (30361201,30458701)

摘要

摘要: 生态学研究发现，多种食饵选择对捕食者-食饵系统的稳定性、持久性等方面有着重要的影响。处于食物链中间层的种群，既是顶层捕食者的食饵，同时又是捕食者，因此中间捕食者的种群数量变化，对整个生态系统有着不可忽略的影响。假设中间捕食者具有其他可供选择的食饵，建立了一个由顶级捕食者、中间捕食者和食饵所构成的三维食物链系统，并对此系统展开动力学分析，推导出系统各个平衡点的存在性和稳定性条件。对Hopf分支的存在性条件进行了深入的分析，并以食饵选择参数为分支参数，对可能出现的Hopf分支情况进行了数值模拟。结合理论和数值结果，分析食饵选择性对食物链系统的稳定性产生的影响。
- 捕食者-食饵模型 /
- 食物链 /
- 可选食饵 /
- 局部渐进稳定 /
- Hopf分支
Abstract: Studies in ecology show that alternative prey has important effects on predator-prey system in the aspects of system stability, species persistence, etc. For species at the intermediate level of a food chain, they are prey of top predators, while predating the bottom prey at the same time. Therefore, the effect of changes in intermediate predators' population on the system cannot be ignored. We set up a three-dimensional food chain model composed of top predator, intermediate predator and prey, assuming that the intermediate predator had alternative choice of prey. The existence and stability of the equilibria were derived through dynamical study of the system. The existence of Hopf bifurcation was explored in depth. The numerical simulations used the prey choice parameter as the bifurcation variable to study the possible Hopf bifurcations. The effect of alternative prey on the stability of the food chain system was derived through the theoretical and numerical results.
- predator-prey model /
- food chain /
- alternative prey /
- locally asymptotically stable /
- Hopf bifurcation

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参考文献(15)

[1]	FREEDMAN H I,WALTMAN P.Mathematical analysis of some three-species food chain models[J].Mathematical Biosciences,1977,33(3):257-276.
[2]	HASTINGS A,POWELL T.Chaos in a three-species food chain[J].Ecology,1991,72(3):896-903.
[3]	HSU S,HWANG T,KUANG Y.A ratio-dependent food chain model and its applications to biological control[J].Mathematical Biosciences,2003,181(1):55-83.
[4]	GINOUX J M,ROSSETTO B,JAMET J L.Chaos in a three-dimensional Volterra-Gause model of predator-prey type[J].International Journal of Bifurcation and Chaos,2005,15(5):1689-1708.
[5]	PATHAK S,MAITI A,SAMANTA G P.Rich dynamics of a food chain model with Hassell-Varley type functional responses[J].Applied Mathematics and Computation,2009,208(2):303-317.
[6]	GEORGE A K,KOOI P I,BOER M P.Ecological consequences of global bifurcations in some food chain models[J].Mathematical Biosciences,2010,226(2):120-133.
[7]	STRAUSS S Y.Indirect effects in community ecology: Their definition,study and importance[J].Trends in Ecological Evolution,1991,6(7): 206-210.
[8]	SAHOO B,PORIA S.Diseased prey predator model with general Holling type interactions[J].Applied Mathematics and Computation,2014,226(1):83-100.
[9]	HUXEL G R,MCCANN K.Food web stability: The influence of trophic flows across habitats[J].American Natualist,1998,152(3):460-469.
[10]	HUXEL G R,MCCANN K,POLIS G A.Effects of partitioning allochthonous and autochthonous resources on food web stability[J].Ecological Research,2002,17(4):419-432.
[11]	SRINIVASU P D N,PRASAD B S R V,VENKATESULU M.Biological control through provision of additional food to predators: A theoretical study[J].Theoretical Population Biology,2007,72(1):111-120.
[12]	SAHOO B.Effects of additional foods to predators on nutrient-consumer-predator food chain model[J/OL].ISRN Biomathematics,2012.http://dx.doi.org/10.5402/2012/796783.
[13]	SAHOO B.Global stability of predator-prey system with alternative prey[J/OL].ISRN biotechnology,2013.http://dx.doi.org/10.5402/2013/898039.
[14]	SAHOO B,PORIA S.Disease control in a food chain model supplying alternative food[J].Applied Mathematical Modelling,2013,37(8):5653-5663.
[15]	SAHOO B,PORIA S.The chaos and control of a food chain model supplying additional food to top-predator[J].Chaos Solitons & Fractals,2014,58(1):52-64.